Influence of the dispersion in model of continuous mechanics

The aim of this book is to clarify the mathematical model describing the mechanics of continuous media and rarefied gas. The present study is associated with the formulation of conservation laws as conditions of equilibrium of angular momentums and forces, while usually formulated in terms of balance of force. The equations for gas are found from the modified Boltzmann equation and the phenomenological theory. For a rigid body the equations are used of the phenomenological theory, but changed their interpretation. We elucidate the contribution of cross-effects in the conservation laws of continuum mechanics, including the self-diffusion, thermal diffusion, etc., which indicated S. Vallander. Resolved the paradox of Hilbert in the solution of the Boltzmann equation by the Chapman-Enskog method. Refined model of the boundary conditions for rarefied gas flows and transient flow near the moving surfaces are discussed. The results of numerical and analytical studies of certain problems of the boundary layer, the interaction of gas flow with the crystal surface for the gas that is moving near the solid surface, the simplest problems of elasticity are discussed.